Mathematics

Activity 1: Our classroom, generation by generation

In this activity, you will generate some statistical activity using resources in the classroom, your families and secondary data sets. There is also the opportunity to use contacts in Asia to access and use additional data sets.

Task 1: Countries of birth in our class

1. Write what you think – make some conjectures – about the following statements and record them.
   • I think the most common country of birth of the students in our class will be …
   • I think there will be … different countries of birth in our class.
   • I think … % of the students in our class will have been born in Australia.
2. Discuss your conjectures as a class.
3. Discuss possible ways of collecting data to answer the questions and test the conjectures. Choose a method of data collection and collect the data.
4. How might we present this data? Choose and use a suitable form of data representation such as a table, column graph, bar chart or pie graph.
5. What are your conclusions?
6. Is there a preferred way of displaying the data? What is it and why?
7. Record a summary of your conclusions. Are there any surprises?

Task 2: Countries of birth of our parents/carers

1. Make some conjectures about the following statements and record them.
   • I think the most common country of birth of the parents/carers of the students in our class will be …
   • I think there will be … different countries of birth of the parents/carers of the students in our class.
   • I think … % of the parents/carers of the students in our class will have been born in Australia.
2. Discuss your conjectures as a class.
3. Discuss possible ways of collecting data to answer the questions and test the conjectures. Choose a method of data collection and collect the data. How might the collected data be organised?
4. You could write the countries of birth of each of your parents/carers on separate sticky notes and place them in the appropriate columns of a class wall chart. This automatically produces a visual display – another representation of the data.
5. Now choose and use a suitable form of data representation such as a table, column graph, bar chart or pie graph.
6. Record a summary of your conclusions.
7. Discuss the findings. Are there any surprises?

Task 3: Countries of birth of our grandparents

If the information is available about grandparents, the size of this data set will have doubled at each step from student, to parents/carers, to grandparents.

1. Write what you think about the following statements and record them.
   • I think the most common country of birth of our grandparents will be …
   • I think there will be … different countries of birth of our grandparents.
   • I think … % of the grandparents of the students in our class will have been born in Australia.
2. Discuss your conjectures as a class.
3. Collate the information. This could be put on a wall chart showing sticky notes categorised under appropriate headings or on a table using tally marks.
4. Choose and construct an appropriate form of graph to display the data.
5. Discuss your findings with the class. Are there any surprises? Record a summary of the conclusions.

Activity 2: Classrooms in the Asia region and our classroom

In this activity you will make a series of assumptions about the countries of birth of students in a classroom in Asia and gather and present data in graphical formats.

Task 1: Make a conjecture

1. What do you think? In countries of the Asia region, do classrooms have students with different countries of birth? Would you expect there to be a greater number of countries of birth in, say, a Hong Kong classroom than in your classroom? Why?
2. Choose a country in Asia and make a conjecture about the following and give your reasons.
   • In a classroom in (your chosen country) I think the most common country of birth will be ...
   • In a classroom in (your chosen country) I think there will be ... different countries of birth.

Task 2: How can we get some data?

1. It may be that you have relatives or friends living in Asia and have email contact with them. Ask them to collect some data for their class. What you need is a list of their classmates and their countries of birth. If no one in the class can collect data from a classroom in Asia, use the Hong Kong schools data as shown below..
2. How could you organise the collected data?
3. How could you present this data? Choose and create a suitable form of data representation, for example a table, column graph, bar chart or pie graph.
4. Discuss the data as a class:
   • What are your conclusions?
   • Record a summary of your conclusions. Are there any surprises?
   • How accurate were the conjectures you made in Task 1?

Task 3: How can we compare the classes?

1. Look at the Hong Kong schools data. How does your class compare with the classes in Hong Kong? Were your earlier conjectures correct? Is there a greater number of countries of birth in the Hong Kong classrooms or in your own?
2. You now have data relating to a number of classes. Discuss the following:
   • How can we present 'our class' data and data from Asian classrooms to display the comparison: for example, by using side by side column or bar graphs, side by side pie graphs or a table showing percentages?
3. Choose a graph type, construct the graph and write about the findings.

Hong Kong schools data 

Class 1

Class 2

Activity 3: Using census data

In this activity you will use census data to graph countries of birth in the Australian population.

Task: Using census data

1. Consider this question: which state or territory has the greatest percentage of students born overseas? Write your conjecture. Remember, the question refers to percentage, not number.
2. Go to the CensusAtSchool website.
   • Under the heading Data select Random sampler
   • Read and accept the conditions of use
   • Complete the on-screen menu …
   • Reference year: 2011 (or another choice)
   • Questions to display: All (or the option of Q3 is available for years after 2010)
   • Sample size 200
   • Sample characteristics: There are several options including postcodes, states and territories. Given we want to compare states and territories, choose your first state: say, New South Wales
   • Select year levels: All
   • Select sex: All
   • Get Data Sample
3. Repeat this process for each state and territory. To share the workload you could work in groups and share your random samples.
4. Complete a table with the state and territory, tally marks, totals and percentages.
5. Given that you will have accessed different samples of 200 students, what variation is there in the percentages? This raises questions about statistical variation.
6. Extension idea: What is the most common Australian state/territory of birth of students in your class? What are your expectations? Will your home state/territory be the most common place of birth? Do you think that will be the case for all states and territories?
   • Collect data in your classroom to test your conjecture.
   • Collect data from the CensusAtSchool database.

Activity 4: A final comparison

In this activity you will use the data from ten top countries of birth to compare changes in the birthplaces of the Australian population over time.

Task: A final comparison

1. Look at Top 10 countries of Birth.
2. As a class discuss the meaning of the numbers in the table.
   • What does a percentage of 0.2% imply?
   • What is the meaning of 'Other'?
   • What does the increase in 'Other' from 1.3 to 9.2 suggest?
   • How variable is the percentage born overseas?
3. In small groups, investigate the table and write down any observations. Your investigations might include:
   • a focus on one half of the table … 1901 or 2006
   • a comparison of the two halves or an aspect of the two halves
   • how numbers have increased between 1901 and 2006 while some percentages have decreased
   • the changing order of countries
   • factors that would have influenced changes over time. For example, some countries have moved into the Top 10, others have dropped out.
4. In your group, make comparisons and reflect on reasons and implications.
5. Present your group's findings to the whole class.
6. As a whole class, discuss the usefulness of the table format and suggest alternative ways of presenting the same information in a graphical form; such as side by side pie graphs, side by side column graphs, picture graphs or a differently formatted table.
7. Select one of the graph forms and create your own graph using the data.
8. Display and compare all graphs and decide on which ones are the most effective.

9. Extension: Complete the table below by calculating the relevant percentages for your class. Comment on any changes in the percentages over the generations.